Solve for $x$ and $y$ using elimination. ${-4x+3y = -7}$ ${-5x+6y = -2}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-2$ ${8x-6y = 14}$ $-5x+6y = -2$ Add the top and bottom equations together. $3x = 12$ $\dfrac{3x}{{3}} = \dfrac{12}{{3}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-4x+3y = -7}\thinspace$ to find $y$ ${-4}{(4)}{ + 3y = -7}$ $-16+3y = -7$ $-16{+16} + 3y = -7{+16}$ $3y = 9$ $\dfrac{3y}{{3}} = \dfrac{9}{{3}}$ ${y = 3}$ You can also plug ${x = 4}$ into $\thinspace {-5x+6y = -2}\thinspace$ and get the same answer for $y$ : ${-5}{(4)}{ + 6y = -2}$ ${y = 3}$